Bertrand Russell

Bertrand Arthur William Russell (1872–1970) was a British
philosopher, logician, essayist and social critic best known for his
work in mathematical logic and analytic philosophy. His most
influential contributions include his championing of logicism (the
view that mathematics is in some important sense reducible to logic),
his refining of Gottlob Frege's predicate
calculus (which still forms the basis of most contemporary systems of
logic), his defense of neutral monism
(the view that the world consists of just one type of substance which
is neither exclusively mental nor exclusively physical), and his
theories of
definite descriptions and
logical atomism.

Together with
G.E. Moore,
Russell is generally recognized as one of the main founders of modern
analytic philosophy. Together with
Kurt Gödel, he is regularly
credited with being one of the most important logicians of the
twentieth century.

Over the course of a long career, Russell also made significant
contributions to a broad range of other subjects, including the
history of ideas, ethics, political
theory, educational theory and religious studies. In addition,
generations of general readers have benefited from his many popular
writings on a wide variety of topics in both the humanities and the
natural sciences. Like Voltaire, to whom he
has been compared, he wrote with style and wit and had
enormous influence.

After a life marked by controversy—including dismissals from
both Trinity College, Cambridge, and City College, New
York—Russell was awarded the Order of Merit in 1949 and the
Nobel Prize for Literature in 1950. Noted also for his many spirited
anti-nuclear protests and for his campaign against western
involvement in the Vietnam War, Russell remained a prominent
public figure until his death at the age of 97.

(1916) Fined 100 pounds and dismissed from Trinity College as a
result of anti-war writings; denied a passport and so unable to
lecture at Harvard.

(1918) Imprisoned for five months as a result of anti-war
writings.

(1921) Divorce from Alys and marriage to Dora Black.

(1922) Runs for parliament and is defeated.

(1923) Runs for parliament and is defeated.

(1927) Opens experimental school with Dora.

(1931) Becomes the third Earl Russell upon the death of his
brother.

(1935) Divorce from Dora.

(1936) Marriage to Patricia (Peter) Helen Spence.

(1938) Appointed visiting professor of philosophy at Chicago.

(1939) Appointed professor of philosophy at the University of
California at Los Angeles.

(1940) Appointment at City College New York revoked prior to
Russell's arrival as the result of public protests and a legal
judgment in which Russell was found to be “morally unfit”
to teach at the college.

(1942) Dismissed from Barnes Foundation in Pennsylvania, but wins
a lawsuit against the Foundation for wrongful dismissal.

(1944) Reappointed a Fellow of Trinity College.

(1949) Awarded the Order of Merit; elected a Lifetime Fellow at
Trinity College.

(1950) Awarded Nobel Prize for Literature.

(1952) Divorce from Patricia (Peter) and marriage to Edith Finch.

(1955) Releases Russell-Einstein Manifesto.

(1957) Elected President of the first Pugwash Conference.

(1958) Becomes founding President of the Campaign for Nuclear
Disarmament.

(1961) Imprisoned for one week in connection with anti-nuclear
protests.

(1963) Establishes the Bertrand Russell Peace Foundation.

(1967) Launches the International War Crimes Tribunal.

(1970) Dies February 02 at Penrhyndeudraeth, Wales.

Attempts to sum up Russell's life have been numerous. One of the more
famous comes from the Oxford
philosopher A.J. Ayer. As Ayer writes,
“The popular conception of a philosopher as one who combines
universal learning with the direction of human conduct was more nearly
satisfied by Bertrand Russell than by any other philosopher of our
time” (1972a, 127). Another telling comment comes from the
Harvard philosopher W.V. Quine: “I
think many of us were drawn to our profession by Russell's books. He
wrote a spectrum of books for a graduated public, layman to
specialist. We were beguiled by the wit and a sense of new-found
clarity with respect to central traits of reality” (1966c, 657).

Despite such comments, perhaps the most memorable encapsulation of
Russell's life and work comes from Russell himself. As Russell tells
us,

Three passions, simple but overwhelmingly strong, have governed my
life: the longing for love, the search for knowledge, and unbearable
pity for the suffering of mankind. These passions, like great winds,
have blown me hither and thither, in a wayward course, over a great
ocean of anguish, reaching to the very verge of despair.

I have sought love, first, because it brings ecstasy – ecstasy
so great that I would often have sacrificed all the rest of life for a
few hours of this joy. I have sought it, next, because it relieves
loneliness – that terrible loneliness in which one shivering
consciousness looks over the rim of the world into the cold
unfathomable lifeless abyss. I have sought it finally, because in the
union of love I have seen, in a mystic miniature, the prefiguring
vision of the heaven that saints and poets have imagined. This is what
I sought, and though it might seem too good for human life, this is
what – at last – I have found.

With equal passion I have sought knowledge. I have wished to
understand the hearts of men. I have wished to know why the stars
shine. And I have tried to apprehend the Pythagorean power by which
number holds sway above the flux. A little of this, but not much, I
have achieved.

Love and knowledge, so far as they were possible, led upward toward
the heavens. But always pity brought me back to earth. Echoes of cries
of pain reverberate in my heart. Children in famine, victims tortured
by oppressors, helpless old people a hated burden to their sons, and
the whole world of loneliness, poverty, and pain make a mockery of
what human life should be. I long to alleviate this evil, but I
cannot, and I too suffer.

This has been my life. I have found it worth living, and would gladly
live it again if the chance were offered me. (1967, 3–4)

By any standard, Russell led an enormously full life. In addition to
his ground-breaking intellectual work in logic and analytic
philosophy, he involved himself for much of his life in politics. As
early as 1904 he spoke out frequently in favour of internationalism
and in 1907 he ran for Parliament. Although he stood as an
independent, he endorsed the full 1907 Liberal platform. He also
advocated extending the franchise to women, provided that such radical
political change was introduced only through constitutional means (Wood
1957, 71). Three years later he published Anti-Suffragist
Anxieties (1910).

With the outbreak of World War I, Russell became involved in anti-war
activities and in 1916 he was fined 100 pounds for authoring an
anti-war pamphlet. Because of his conviction, he was dismissed from
his post at Trinity College, Cambridge (Hardy 1942). Two years later,
he was convicted a second time, this time for suggesting that American
troops might be used to intimidate strikers in Britain (Clark 1975,
337-339). The result was five months in Brixton Prison as prisoner
No. 2917 (Clark 1975). In 1922 and 1923 Russell ran twice more for
Parliament, again unsuccessfully, and together with his second wife,
Dora, he founded an experimental school that they operated during the
late 1920s and early 1930s (Russell 1926 and Park 1963). Perhaps not
surprisingly, some of Russell's more radical activities –
including his advocacy of post-Victorian sexual practices – were
linked in many people's minds to his atheism, made famous in part by
his 1948 BBC debate with the Jesuit philosopher Frederick Copleston
over the existence of God.

Although Russell became the third Earl Russell upon the death of his
brother in 1931, Russell's radicalism continued to make him a
controversial figure well through middle-age. While teaching at UCLA
in the United States in the late 1930s, he was offered a teaching
appointment at City College, New York. The appointment was revoked
following a series of protests and a 1940 judicial decision which
found him morally unfit to teach at the College (Dewey and Kallen
1941, Irvine 1996, Weidlich 2000). The legal decision had been based partly
on Russell's atheism and partly on his fame as an advocate of free
love and open marriages.

In 1954 Russell delivered his famous “Man's Peril” broadcast on
the BBC, condemning the Bikini H-bomb tests. A year later, together
with Albert Einstein, he released the Russell-Einstein Manifesto
calling for the curtailment of nuclear weapons. In 1957 he became a prime
organizer of the first Pugwash Conference, which brought together a
large number of scientists concerned about the nuclear issue. He
became the founding president of the Campaign for Nuclear Disarmament
in 1958 and Honorary President of the Committee of 100 in
1960.

In 1961, Russell was once again imprisoned, this time for a week in
connection with anti-nuclear protests. The media coverage surrounding
his conviction only served to enhance Russell's reputation and to
further inspire the many idealistic youths who were sympathetic to his
anti-war and anti-nuclear message. Beginning in 1963, he began work on
a variety of additional issues, including lobbying on behalf of
political prisoners under the auspices of the Bertrand Russell Peace
Foundation.

Interestingly, throughout much of his life Russell saw himself
primarily as a writer rather than as a philosopher, listing
“Author” as his profession on his passport. As he says in
his Autobiography, “I resolved not to adopt a
profession, but to devote myself to writing” (1967, 125). Upon
being awarded the Nobel Prize for Literature in 1950, Russell used his
acceptance speech to emphasize themes relating to his
social activism.

Over the years, Russell has served as the subject of numerous
creative works, including T.S. Eliot's “Mr Appolinax”
(1917), D.H. Lawrence's “The Blind Man” (1920), Aldous
Huxley's Chrome Yellow (1921), Bruce Duffy's The
World as I Found It (1987) and the graphic novel by Apostolos
Doxiadis and Christos Papadimitriou, Logicomix: An Epic Search
for Truth (2009).

Readers wanting additional information about Russell's life are
encouraged to consult Russell's five autobiographical volumes:
Portraits from Memory and other Essays (A1956b),
My Philosophical Development (1959) and The
Autobiography of Bertrand Russell (3 vols, 1967, 1968,
1969). In addition, John Slater's accessible Bertrand
Russell (1994) gives a short but informative introduction to
Russell's life, work and influence. Other sources of biographical
information include Ronald Clark's authoritative The Life of
Bertrand Russell (1975), Ray Monk's two volumes,
Bertrand Russell: The Spirit of Solitude (1996) and
Bertrand Russell: The Ghost of Madness (2000), and the
first volume of Andrew Irvine's Bertrand Russell: Critical
Assessments (1999).

For a chronology of Russell's major publications, readers are
encouraged to consult the Primary Literature
section of the Bibliography below. For a complete, descriptive
bibliography, see A Bibliography of Bertrand Russell (3
vols, 1994), by Kenneth Blackwell and Harry Ruja. A less detailed list
appears in Paul Arthur Schilpp, The Philosophy of Bertrand
Russell (1944).

For a detailed bibliography of the secondary literature surrounding
Russell up to the close of the twentieth century, see Andrew
Irvine, Bertrand Russell: Critical Assessments, Vol. 1
(1999). For a list of new and forthcoming books relating to Russell,
see the
Forthcoming Books
page at the Bertrand Russell Archives.

Russell's main contributions to logic and the foundations of
mathematics include his discovery of
Russell's paradox
(also known as the Russell-Zermelo paradox), his development of the
theory of types, his championing of
logicism (the view that mathematics is, in some significant sense,
reducible to formal logic), his impressively general theory of logical
relations, his formalization of the mathematics of quantity and of the
real numbers, and his refining of the first-order predicate
calculus.

Russell discovered the paradox that bears his name in 1901, while
working on his Principles of Mathematics (1903). The
paradox arises in connection with the set of all sets that are not
members of themselves. Such a set, if it exists, will be a member of
itself if and only if it is not a member of itself. In his 1901 draft
of the Principles of Mathematics, Russell summarizes the
problem as follows:

The axiom that all referents with respect to a given relation form a
class seems, however, to require some limitation, and that for the
following reason. We saw that some predicates can be predicated of
themselves. Consider now those … of which this is not the
case. … [T]here is no predicate which attaches to all of them
and to no other terms. For this predicate will either be predicable or
not predicable of itself. If it is predicable of itself, it is one of
those referents by relation to which it was defined, and therefore, in
virtue of their definition, it is not predicable of
itself. Conversely, if it is not predicable of itself, then again it
is one of the said referents, of all of which (by hypothesis) it is
predicable, and therefore again it is predicable of itself. This is a
contradiction. (CP, Vol. 3, 195)

The paradox is significant since, using classical logic, all sentences
are entailed by a contradiction. Russell's discovery thus prompted a
large amount of work in logic, set theory, and the
philosophy and foundations of mathematics.

Russell's response to the paradox
came between 1903 and 1908 with the development of his
theory of types. It was clear to Russell
that some form of restriction needed to be placed on the original
comprehension (or abstraction) axiom of naïve set theory, the
axiom that formalizes the intuition that any coherent condition (or
property) may be used to determine a set. Russell's basic idea was that
reference to sets such as the so-called Russell set (the set of all
sets that are not members of themselves) could be avoided by arranging
all sentences into a hierarchy, beginning with sentences about
individuals at the lowest level, sentences about sets of individuals
at the next lowest level, sentences about sets of sets of individuals
at the next lowest level, and so on. Using a vicious circle principle
similar to that adopted by the mathematician Henri Poincaré,
together with his so-called “no class” theory of classes
(in which class terms gain meaning only when placed in the appropriate
context), Russell was able to explain why the unrestricted
comprehension axiom
fails: propositional functions,
such as the function “x is a set,”
may not be applied to themselves since self-application would involve
a vicious circle. As a result, all objects for which a given condition
(or predicate) holds must be at the same level or of the same
“type.” Sentences about these objects will then always be
higher in the hierarchy than the objects themselves.

Although first introduced in 1903, the theory of types was further
developed by Russell in his 1908 article “Mathematical Logic as Based
on the Theory of Types” and in the three-volume work he co-authored with
Alfred North Whitehead,
Principia Mathematica
(1910, 1912, 1913).
The theory thus admits of two versions, the “simple
theory” of 1903 and the “ramified theory” of
1908. Both versions of the theory came under attack: the simple theory
for being too weak, the ramified theory for being too strong. For
some, it was important that any proposed solution be comprehensive
enough to resolve all known paradoxes at once. For others, it was
important that any proposed solution not disallow those parts of
classical mathematics that remained consistent, even though they
appeared to violate the vicious circle principle. For discussion of
related paradoxes, see Chapter 2 of the Introduction to Whitehead and
Russell (1910), as well as the entry on
paradoxes and contemporary logic in this encyclopedia.

Russell himself had recognized several of these same concerns as early
as 1903, noting that it was unlikely that any single solution would
resolve all of the known paradoxes. Together with Whitehead, he was
also able to introduce a new axiom, the axiom of reducibility, which
lessened the vicious circle principle's scope of application and so
resolved many of the most worrisome aspects of type theory. Even so,
many critics claimed that the axiom was simply too ad hoc to be
justified philosophically. For additional discussion see Linsky
(1990), Linsky (2002) and Wahl (2011).

Of equal significance during this period was Russell's defense of
logicism, the theory that mathematics is in some important sense
reducible to logic. First defended in his 1901 article “Recent
Work on the Principles of Mathematics,” and later in greater
detail in his Principles of Mathematics and in
Principia Mathematica, Russell's logicism consisted of
two main theses. The first was that all mathematical truths can be
translated into logical truths or, in other words, that the vocabulary
of mathematics constitutes a proper subset of the vocabulary of
logic. The second was that all mathematical proofs can be recast as
logical proofs or, in other words, that the theorems of mathematics
constitute a proper subset of the theorems of logic. As Russell
summarizes, “The fact that all Mathematics is Symbolic Logic is
one of the greatest discoveries of our age; and when this fact has
been established, the remainder of the principles of mathematics
consists in the analysis of Symbolic Logic itself” (1903,
5).

Like
Gottlob Frege,
Russell's basic idea for defending logicism was that numbers may be
identified with classes of classes and that number-theoretic
statements may be explained in terms of quantifiers and identity. Thus
the number 1 is to be identified with the class of all unit classes,
the number 2 with the class of all two-membered classes, and so
on. Statements such as “There are at least two books”
would be recast as statements such as “There is a
book, x, and there is a book,
y, and x is not identical to y.”
Statements such as “There are exactly two books” would be
recast as “There is a book, x, and there is a book,
y, and x is not identical to y, and if
there is a book, z, then z is identical to
either x or y.” It follows that
number-theoretic operations may be explained in terms of set-theoretic
operations such as intersection, union, and difference. In
Principia Mathematica, Whitehead and Russell were able
to provide many detailed derivations of major theorems in set theory,
finite and transfinite arithmetic, and elementary measure theory. They
were also able to develop a sophisticated theory of logical relations
and a unique method of founding the real numbers. Even so, the issue
of whether set theory itself can be said to have been successfully
reduced to logic remained controversial. A fourth volume on geometry
was planned but never completed.

Russell's most important writings relating to these topics include not
only his Principles of Mathematics (1903),
“Mathematical Logic as Based on the Theory of Types”
(1908), and Principia Mathematica (1910, 1912, 1913),
but also his earlier Essay on the Foundations of
Geometry (1897) and his Introduction to Mathematical
Philosophy (1919a), the last of which was written while Russell
was serving time in Brixton Prison as a result of his anti-war
activities. Coincidentally, it was at roughly this same time
that Ludwig Wittgenstein, Russell's
most famous pupil, was completing his Tractatus
Logico-Philosophicus (1921) while being detained as a prisoner
of war at Monte Cassino in Italy during World War I.

Anyone needing
assistance in deciphering the symbolism found in the more technical of
Russell's writings is encouraged to consult
the Notation in Principia
Mathematica entry in this encyclopedia.

In much the same way that Russell used logic in an attempt to clarify
issues in the foundations of mathematics, he also used logic in an
attempt to clarify issues in philosophy. As one of the founders of
analytic philosophy, Russell made significant contributions to a wide
variety of areas, including metaphysics,
epistemology, ethics and political
theory. His advances in logic and metaphysics also had significant
influence on Rudolf Carnap and the
Vienna Circle.

According to Russell, it is the philosopher's job to discover a
logically ideal language — a language that will exhibit the
nature of the world in such a way that we will not be misled by the
accidental, imprecise surface structure of natural language. As
Russell writes, “Ordinary language is totally unsuited for
expressing what physics really asserts, since the words of everyday
life are not sufficiently abstract. Only mathematics and mathematical
logic can say as little as the physicist means to say” (1931,
82). Just as atomic facts (the association of properties and relations
with individuals) combine to form molecular facts in the world itself,
such a language will allow for the description of such combinations
using logical connectives such as “and” and
“or.” In addition to the existence of atomic and molecular
facts, Russell also held that general facts (facts about
“all” of something) are needed to complete our picture of
the world. Famously, he vacillated on whether negative facts were also
required.

The reason Russell believes many ordinarily accepted statements are
open to doubt is that they appear to refer to entities that may be
known only through inference. Thus, underlying Russell's various projects
was not only his use of logical analysis, but also his long-standing
aim of discovering whether, and to what extent, knowledge is
possible. “There is one great question,” he writes in
1911. “Can human beings know anything, and if so, what
and how? This question is really the most essentially philosophical of
all questions” (quoted in Slater 1994, 67).

Motivating this question was the traditional problem of the external
world. If our knowledge of the external world comes through inferences
to the best explanation, and if such inferences are always fallible,
what guarantee do we have that our beliefs are reliable? Russell's
response to this question was partly metaphysical and partly
epistemological. On the metaphysical side, Russell developed his
famous theory of logical atomism, in
which the world is said to consist of a complex of logical atoms (such
as “little patches of colour”) and their properties and
relations. (The theory was crucial for influencing
Wittgenstein's theory
of the same name.) Together these atoms and their
properties form the atomic facts which, in turn, combine to form
logically complex objects. What we normally take to be inferred
entities (for example, enduring physical objects) are then understood
as logical constructions formed
from the immediately given entities of sensation, viz.,
“sensibilia.”

On the epistemological side, Russell argues that it is also important
to show how each questionable entity may be reduced to, or defined in
terms of, another entity (or entities) whose existence is
more certain. For example, on this view, an ordinary physical object
that normally might be thought to be known only through inference may
be defined instead

as a certain series of appearances, connected with each
other by continuity and by certain causal laws. … More
generally, a ‘thing’ will be defined as a certain series
of aspects, namely those which would commonly be said to
be of the thing. To say that a certain aspect is an
aspect of a certain thing will merely mean that it is one of
those which, taken serially, are the thing. (1914a,
106–107)

The reason we are able to do this, says Russell, is that

our world is not
wholly a matter of inference. There are things that we know without
asking the opinion of men of science. If you are too hot or too cold,
you can be perfectly aware of this fact without asking the physicist
what heat and cold consist of. … We may give the name
‘data’ to all the things of which we are aware without
inference. (1959, 23)

We can then use these data (or “sensibilia” or
“sense data”) with which we
are directly acquainted to construct the relevant objects of
knowledge. Similarly, numbers may be reduced to collections of
classes; points and instants may be reduced to ordered classes of
volumes and events; and classes themselves may be reduced to
propositional functions.

It is with these kinds of examples in mind that Russell suggests
we adopt what he calls “the supreme maxim in scientific
philosophizing,” namely the principle that “Whenever
possible, logical constructions,” or as he also sometimes puts
it, “logical fictions,” are “to be substituted for inferred
entities” (1914c, 155; cf. 1914a, 107, and 1924, 326). Anything
that resists construction in this sense may be said to be an
ontological atom. Such objects are atomic, both in the sense that they
fail to be composed of individual, substantial parts, and in the sense
that they exist independently of one another. Their corresponding
propositions are also atomic, both in the sense that they contain no
other propositions as parts, and in the sense that the members of any
pair of true atomic propositions will be logically independent of one
another. Russell believes that formal logic, if carefully developed, will
mirror precisely, not only the various relations between all such
propositions, but their various internal structures as well.

It is in this context that Russell also introduces his famous
distinction between two kinds of knowledge of truths: that which is
direct, intuitive, certain and infallible, and that which is indirect,
derivative, uncertain and open to error (1905, 41f; 1911, 1912, and
1914b). To be justified, every indirect knowledge claim must be
capable of being derived from more fundamental, direct or intuitive
knowledge claims. The kinds of truths that are capable of being known
directly include both truths about immediate facts of sensation and
truths of logic. Additional examples are discussed in The
Problems of Philosophy (1912a) where Russell states that
propositions with the highest degree of self-evidence (what he here
calls “intuitive knowledge”) include “those which
merely state what is given in sense, and also certain abstract logical
and arithmetical principles, and (though with less certainty) some
ethical propositions” (1912a, 109).

Eventually, Russell supplemented this distinction between direct and
indirect knowledge of truths with his equally famous distinction
between knowledge by acquaintance and knowledge by description. As
Russell explains, “I say that I am acquainted with an object
when I have a direct cognitive relation to that object, i.e. when I am
directly aware of the object itself. When I speak of a cognitive
relation here, I do not mean the sort of relation which constitutes
judgment, but the sort which constitutes presentation” (1911,
209). Later, he clarifies this point by adding that acquaintance
involves, not knowledge of truths, but knowledge of things (1912a,
44). Thus, while intuitive knowledge and derivative knowledge both
involve knowledge of propositions (or truths), knowledge by
acquaintance and knowledge by description both involve knowledge of
things (or objects). This distinction is slightly complicated by the
fact that, even though knowledge by description is in part based upon
knowledge of truths, it is still knowledge of things, and not of
truths. (I am grateful to Russell Wahl for reminding me of this
point.) Since it is things with which we have direct acquaintance
that are the least questionable members of our ontology, it is these
objects upon which Russell ultimately bases his epistemology.

Also relevant was Russell's reliance upon his so-called regressive
method (Irvine 1989, Mayo-Wilson 2011) and his eventual abandoning of
foundationalism in favour of a more recognizably coherentist approach
to knowledge (Irvine 2004). As Russell puts it, even in logic and
mathematics

We tend to believe the premises because we can see that their
consequences are true, instead of believing the consequences because
we know the premises to be true. But the inferring of premises from
consequences is the essence of induction; thus the method in
investigating the principles of mathematics is really an inductive
method, and is substantially the same as the method of discovering
general laws in any other science. (1907, 273-274)

Russell's contributions to metaphysics and epistemology are also
unified by his views concerning the centrality of both scientific
knowledge and the importance of there being an underlying methodology
common to both philosophy and science. In the case of philosophy, this
methodology expresses itself through Russell's use of logical analysis
(Hager 1994, Irvine 2004). In fact, Russell often claims that he has
more confidence in his methodology than in any particular
philosophical conclusion.

This broad conception of philosophy arose in part from Russell's
idealist origins (Hylton 1990a, Griffin 1991). This is so, even though
Russell tells us that his one, true revolution in philosophy came
as a result of his break from idealism. Russell saw that the
idealist doctrine of internal relations led to a series of
contradictions regarding asymmetrical (and other) relations necessary
for mathematics. As he reports,

It was towards the end of 1898 that Moore and I rebelled
against both Kant and Hegel. Moore led the way, but I followed closely
in his footsteps. … [Our rebellion centred upon] the doctrine that
fact is in general independent of experience. Although we were in
agreement, I think that we differed as to what most interested us in
our new philosophy. I think that Moore was most concerned with the
rejection of idealism, while I was most interested in the rejection of
monism. (1959, 54)

The two ideas were closely connected through the so-called doctrine of
internal relations. In contrast to this doctrine, Russell proposed his own new doctrine
of external relations:

The doctrine of internal relations held that every relation between
two terms expresses, primarily, intrinsic properties of the two terms
and, in ultimate analysis, a property of the whole which the two
compose. With some relations this view is plausible. Take, for
example, love or hate. If A loves B, this relation exemplifies itself
and may be said to consist in certain states of mind of A. Even an
atheist must admit that a man can love God. It follows that love of
God is a state of the man who feels it, and not properly a relational
fact. But the relations that interested me were of a more abstract
sort. Suppose that A and B are events, and A is earlier than B. I do
not think that this implies anything in A in virtue of which,
independently of B, it must have a character which we inaccurately
express by mentioning B. Leibniz gives an extreme example. He says
that, if a man living in Europe has a wife in India and the wife dies
without his knowing it, the man undergoes an intrinsic change at the
moment of her death. (1959, 54)

This is the type of doctrine Russell opposed, especially with respect
to the asymmetrical relations necessary for mathematics. For example,
consider two numbers, one of which is found earlier than the other in
a given series:

If A is earlier than B, then B is not earlier than A. If you try to
express the relation of A to B by means of adjectives of A and B, you
will have to make the attempt by means of dates. You may say that the
date of A is a property of A and the date of B is a property of B, but
that will not help you because you will have to go on to say that the
date of A is earlier than the date of B, so that you will have found
no escape from the relation. If you adopt the plan of regarding the
relation as a property of the whole composed of A and B, you are in a
still worse predicament, for in that whole A and B have no order and
therefore you cannot distinguish between “A is earlier than
B” and “B is earlier than A.” As asymmetrical
relations are essential in most parts of mathematics, this doctrine
was important. (1959, 54–55)

Thus, by the end of 1898 Russell had abandoned the idealism that he
had been encouraged to adopt as a student at Cambridge, along with his
original Kantian methodology. In its place he adopted a new,
pluralistic realism. As a result, he soon
became famous as an advocate of “the new realism” and of
his “new philosophy of logic,” emphasizing as he did the
importance of modern logic for philosophical analysis. The underlying
themes of this revolution included Russell's belief in pluralism, his
emphasis on anti-psychologism and his belief in the importance of
science. Each of these themes remained central to his philosophy for
the remainder of his life (Hager 1994, Weitz 1944).

Russell's most important writings relating to these topics include
Knowledge by Acquaintance and Knowledge by Description
(1911), The Problems of Philosophy (1912a), “Our
Knowledge of the External World” (1914a), On the Nature
of Acquaintance (1914b, published more completely
in Collected Papers, Vol. 7), “The Philosophy of
Logical Atomism” (1918, 1919), “Logical Atomism”
(1924), The Analysis of Mind (1921), The Analysis
of Matter (1927a), Human Knowledge: Its Scope and
Limits (1948), and Theory of Knowledge (CP,
Vol. 7).

Russell's philosophical method has at its core the making and testing of
hypotheses through the weighing of evidence. Hence Russell's comment
that he wished to emphasize the “scientific method” in
philosophy. His method also requires the rigorous
analysis of problematic propositions using the machinery of
first-order logic. It was Russell's belief that by using the new logic
of his day, philosophers would be able to exhibit the underlying
“logical form” of natural-language statements. A
statement's logical form, in turn, would help resolve various
problems of reference associated with the ambiguity and vagueness of
natural language.

Since the introduction of the modern predicate calculus, it has been common to use three separate logical notations
(“Px”, “x = y”, and
“∃x”) to represent three separate senses of the natural-language word “is”: the is of predication, e.g. “Cicero is wise”;
the is of identity, e.g. “Cicero is Tully”; and
the is of existence, e.g. “Cicero is”. It was Russell's suggestion that, just as we use logic to make clear these distinctions, we can also use logic to discover
other ontologically significant distinctions, distinctions that should be reflected in the analysis we give of each sentence's correct logical form.

On Russell's view, the subject matter
of philosophy is then distinguished from that of the sciences only by
the generality and a prioricity of philosophical statements,
not by the underlying methodology of the discipline. In philosophy,
just as in mathematics, Russell believed that it was by applying
logical machinery and insights that advances in analysis would be
made.

Russell's most famous example of his new “analytic method”
concerns so-called denoting phrases, phrases that include
both definite descriptions and proper
names. Like
Alexius Meinong, Russell had initially
adopted the view that every denoting phrase (for example,
“Scott,” “the author of
Waverley,” “the number two,”
“the golden mountain”) denoted, or referred to, an
existing entity. On this view, even fictional and imaginary entities
had to be real in order to serve as truth-makers for true sentences
such as “Unicorns have exactly one horn.” By the time his
landmark article, “On Denoting,” appeared in 1905, Russell
had modified his extreme realism, substituting in its place the view
that denoting phrases need not possess a theoretical unity. As Russell
puts it, the assumption that every denoting phrase must refer to an
existing entity was the type of assumption that exhibited “a
failure of that feeling for reality which ought to be preserved even
in the most abstract studies” (1919a, 165).

While logically proper names (words such as “this” or
“that” which refer to sensations of which an agent is
immediately aware) do have referents associated with them, descriptive
phrases (such as “the smallest number less than pi”)
should be viewed merely as collections of quantifiers (such as
“all” and “some”) and
propositional functions
(such as “x is a number”). As such, they are not
to be viewed as referring terms but, rather, as “incomplete
symbols.” In other words, they are to be viewed as symbols that
take on meaning within appropriate contexts, but that remain meaningless
in isolation.

Put another way, it was Russell's insight that some phrases may
contribute to the meaning (or reference) of a sentence without
themselves being meaningful. As he explains,

If “the author of Waverley” meant anything other
than “Scott”, “Scott is the author
of Waverley” would be false, which it is not. If
“the author of Waverley” meant
“Scott”, “Scott is the author
of Waverley” would be a tautology, which it is
not. Therefore, “the author of Waverley” means
neither “Scott” nor anything else – i.e. “the
author of Waverley” means nothing, Q.E.D. (1959,
85)

If Russell is correct, it follows that in a sentence such as

(1) The present King of France is bald,

the definite description “The present King of France”
plays a role quite different from the role a proper name such as
“Scott” plays in the sentence

(2) Scott is bald.

Letting K abbreviate the predicate “is a present King
of France” and B abbreviate the predicate “is
bald,” Russell assigns sentence (1) the logical form

(1′) There is an x such that

Kx,

for any y, if Ky then y=x, and

Bx.

Alternatively, in the notation of the predicate calculus, we write

(1″)
∃x[(Kx &
∀y(Ky
→
y=x)) &
Bx].

In contrast, by allowing s to abbreviate the name
“Scott,” Russell assigns sentence (2) the very different
logical form

(2′)
Bs.

This distinction between logical forms allows Russell to explain three
important puzzles.

The first concerns the operation of the Law of Excluded Middle and how
this law relates to denoting terms. According to one reading of the
Law of Excluded Middle, it must be the case that either “The
present King of France is bald” is true or “The present
King of France is not bald” is true. But if so, both sentences
appear to entail the existence of a present King of France, clearly an
undesirable result. Russell's analysis shows how this conclusion can
be avoided. By appealing to analysis (1′′), it follows
that there is a way to deny (1) without being committed to the
existence of a present King of France, namely by changing the scope of
the negation operator and thereby accepting that “It is not the
case that there exists a present King of France who is bald” is
true.

The second puzzle concerns the Law of Identity as it operates in
(so-called) opaque contexts. Even though “Scott is the author of
Waverley” is true, it does not follow that the two
referring terms “Scott” and “the author
of Waverley” need be interchangeable in every
situation. Thus, although “George IV wanted to know whether
Scott was the author of Waverley” is true,
“George IV wanted to know whether Scott was Scott” is,
presumably, false.

Russell's distinction between the logical forms associated with the
use of proper names and definite descriptions again shows why this is
so. To see this we once again let s abbreviate the name
“Scott.” We also let w abbreviate
“Waverley” and
A abbreviate the two-place predicate “is the author
of.” It then follows that the sentence

(3) s=s

is not at all equivalent to the sentence

(4)
∃x[(Axw
&
∀y(Ayw
→
y=x)) &
x=s].

Sentence (3), for example, is a necessary truth, while
sentence (4) is not.

The third puzzle relates to true negative existential claims, such as
the claim “The golden mountain does not exist.” Here, once
again, by treating definite descriptions as having a logical form
distinct from that of proper names, Russell is able to give an account
of how a speaker may be committed to the truth of a negative
existential without also being committed to the belief that the
subject term has reference. That is, the claim that Scott does not
exist is false since

(5)
~∃x(x=s)

is self-contradictory. (After all, there must exist at least one thing
that is identical to s since it is a logical truth that
s is identical to itself!) In contrast, the claim that a
golden mountain does not exist may be true since, assuming that
G abbreviates the predicate “is golden” and M
abbreviates the predicate “is a mountain,” there is nothing
contradictory about

(6)
~∃x(Gx
& Mx).

Russell's most important writings relating to his theory of
descriptions include not only “On Denoting” (1905), but
also The Principles of Mathematics (1903),
Principia Mathematica (1910) and Introduction to
Mathematical Philosophy (1919). (See too Kaplan 1970, Kroon
2009 and Stevens 2011.)

Yet another of Russell's major contributions is his defence
of neutral monism, the view that the
world consists of just one type of substance which is neither
exclusively mental nor exclusively physical. Like idealism (the view
that nothing exists but the mental) and physicalism (the view
that nothing exists but the physical), neutral monism rejects
dualism (the view that there exist distinct mental and physical
substances). However, unlike both idealism and physicalism, neutral
monism holds that this single existing substance may be viewed in some
contexts as being mental and in others as being physical. As Russell
puts it,

“Neutral monism”—as opposed to
idealistic monism and materialistic monism—is the theory that
the things commonly regarded as mental and the things commonly
regarded as physical do not differ in respect of any intrinsic
property possessed by the one set and not by the other, but differ
only in respect of arrangement and
context. (CP, Vol. 7, 15)

To help understand this general suggestion, Russell introduces his
analogy of a postal directory:

The theory may be illustrated by comparison with a postal
directory, in which the same names come twice over, once in
alphabetical and once in geographical order; we may compare the
alphabetical order to the mental, and the geographical order to the
physical. The affinities of a given thing are quite different in the
two orders, and its causes and effects obey different laws. Two
objects may be connected in the mental world by the association of
ideas, and in the physical world by the law of gravitation. …
Just as every man in the directory has two kinds of neighbours, namely
alphabetical neighbours and geographical neighbours, so every object
will lie at the intersection of two causal series with different laws,
namely the mental series and the physical
series. ‘Thoughts’ are not different in substance from
‘things’; the stream of my thoughts is a stream of things,
namely of the things which I should commonly be said to be thinking
of; what leads to its being called a stream of thoughts is merely that
the laws of succession are different from the physical
laws. (CP, Vol. 7, 15)

In other words, when viewed as being mental, a thought or idea may
have associated with it other thoughts or ideas that seem related even
though, when viewed as being physical, they have very little in
common. As Russell explains, “In my mind, Caesar may call up
Charlemagne, whereas in the physical world the two were widely
sundered” (CP, Vol. 7, 15). Even so, it is a mistake, on this
view, to postulate two distinct types of thing (the idea of Caesar
and the man Caesar) that are composed of two distinct substances (the
mental and the physical). Instead, “The whole duality of mind
and matter, according to this theory, is a mistake; there is only one
kind of stuff out of which the world is made, and this stuff is called
mental in one arrangement, physical in the other” (CP, Vol. 7,
15).

Russell appears to have developed this theory around 1913, while
working on his Theory of Knowledge manuscript and on
his 1914 Monist article, “On the Nature of
Acquaintance.” Decades later, in 1964, he remarked that “I
am not conscious of any serious change in my philosophy since I
adopted neutral monism” (Eames 1967, 511). Even so, over the
next several decades Russell continued to do a large amount of
original work, authoring such important books as The Analysis
of Mind (1921), The Analysis of Matter (1927a),
An Inquiry into Meaning and Truth (1940) and
Human Knowledge: Its Scope and Limits (1948).

Today several authors, including David Chalmers (1996, 155) and Thomas Nagel (2002, 209), have shown renewed interest in considering Russell's general approach to the mind.

In addition to the above titles by Russell, Russell's most influential writings
relating to his theories of metaphysics and epistemology include
Our Knowledge of the External World (1914a), “The
Relation of Sense-Data to Physics” (1914c), “The
Philosophy of Logical Atomism” (1918, 1919), “On
Propositions: What They Are and How They Mean” (1919b) and
An Outline of Philosophy (1927b).

Russell's significant social influence stems from three main sources:
his long-standing social activism, his many writings on the social and
political issues of his day as well as on more theoretical concerns,
and his popularizations of numerous technical writings in philosophy
and the natural sciences.

Among Russell's many popularizations are his two best-selling works,
The Problems of Philosophy (1912) and A History
of Western Philosophy (1945). Both of these books, as well as
his numerous books popularizing science, have done much to educate and
inform generations of general readers. His History is
still widely read and did much to initiate twentieth-century research
on a wide range of historical figures from
the presocratics
to Leibniz. His Problems is
still used as an introductory textbook over a century after it was
first published. Both books can be read by the layman with
satisfaction. Other popular books, particularly those relating to
developments in modern science such as
The ABC of Atoms (1923a) and The ABC of
Relativity (1925), are now of more historical interest. Even
so, they continue to convey something of the intellectual excitement associated with
advances in twentieth-century science and philosophy.

Naturally enough, Russell saw
a link between education in this broad sense and social progress. As
he put it, “Education is the key to the new world” (1926,
83). Partly this is due to our need to understand nature, but equally
important is our need to understand each other:

The thing, above all, that a teacher should endeavor to produce in his
pupils, if democracy is to survive, is the kind of tolerance that
springs from an endeavor to understand those who are different from
ourselves. It is perhaps a natural human impulse to view with horror
and disgust all manners and customs different from those to which we
are used. Ants and savages put strangers to death. And those who have
never traveled either physically or mentally find it difficult to
tolerate the queer ways and outlandish beliefs of other nations and
other times, other sects and other political parties. This kind of
ignorant intolerance is the antithesis of a civilized outlook, and is
one of the gravest dangers to which our overcrowded world is
exposed. (1950, 121)

It is in this same context that Russell is famous for suggesting that
a widespread reliance upon evidence, rather than superstition,
would have enormous social consequences: “I wish to propose for
the reader's favourable consideration,” says Russell, “a
doctrine which may, I fear, appear wildly paradoxical and
subversive. The doctrine in question is this: that it is undesirable
to believe a proposition when there is no ground whatever for
supposing it true” (A1928, 11).

Unlike Russell's views about the importance of education, the precise
connection between Russell's political activism and his more
theoretical work has been more controversial. In part, this has been
because Russell himself repeatedly maintained that he saw no
significant connection between his philosophical work and his
political activism. Others have seen things differently. One of the
best summaries is given by Alan Wood:

Russell sometimes maintained, partly I think out of perverseness, that
there was no connection between his philosophical and political
opinions. … But in fact I think there are perfectly obvious
connections between Russell's philosophical and other views. …
To begin with, it is natural enough to find an analytic anti-monist
philosopher like Russell upholding the individual against the state,
whereas Hegel did the reverse … [In addition, the] whole bent
of Russell's mind in philosophy was an attempt to eliminate the a
priori and to accentuate the empirical; and there was exactly the
same trend in his political thinking … Unless it is realized
that Russell's approach to political questions was usually empirical
and practical, based on the evidence of the moment and not on a
priori principles and preconceptions, it is quite impossible to
understand why his views appeared to vary so much. This was perfectly
legitimate, and even praiseworthy, in a world which never stays the
same, and where changing circumstances continually change the balance
of arguments on different sides. (Wood 1957, 73-4)

Thus, in addition to Russell's numerous contributions to the
politics of his day, he also contributed significantly to our
understanding of the social world around us. Among Russell's more
theoretical contributions were his anticipation of John Mackie's error
theory in ethics, the view that moral judgments are cognitive (that
is, they are either true or false), but because of their content they
are in fact inevitably false. (Mackie's paper “The Refutation of
Morals” appeared in 1946; Russell's paper “Is There an
Absolute Good?”, although not published until 1988 was first
delivered in 1922.)

Russell also anticipated the modern theory of
emotivism (as introduced by A.J. Ayer in his 1936 Language, Truth and
Logic), arguing that “Primarily, we call something
‘good’ when we desire it, and ‘bad’ when we
have an aversion from it” (1927b, 242), a view that “he
had been flirting with since 1913” (see the entry
on Russell's Moral Philosophy in this
encyclopedia; see too Schilpp 1944, 719f). Even so, Russell remained
less than satisfied with his views on meta-ethics for most of his life
(CP, Vol. 11, 310).

This dissatisfaction appears not to have extended to his work in
political theory. There Russell focused primarily on the notion of
power, or what he called “the production of intended
effects” (1938, 35). As a result, as V.J. McGill writes,
“The concept of power overshadows all of Russell's political and
economic writings” (Schilpp 1944, 581). As Russell summarizes,
“The laws of social dynamics are – so I shall content
– only capable of being stated in terms of power in its various
forms” (1938, 15). As a result, it is only by understanding
power in all its human instantiations that we understand the social
world around us.

Russell's cataloging of the perceived evils of his age are well
known. Even so, underlying his criticism of both the political left
and the political right lies a common worry: the unequal distribution
of power. As McGill sums up, “Evidently he has become convinced
that the thirst for Power is the primary danger of mankind, that
possessiveness is evil mainly because it promotes the power of man
over man” (Schilpp 1944, 581). The problem with this analysis
and of Russell's desire for a more equitable distribution of power is
that any proposed solution appears to lead to paradox:

Suppose certain men join a movement to disestablish Power, or to
distribute it more equally among the people! If they are successful,
they carry out the behest of Power, becoming themselves as powerful,
in terms of Mr. Russell's definition, as any tyrant. Even though they
spread the good life to millions, the more successful they are, the
more usurpatious and dangerous. (Schilpp 1944, 586)

More than any of his other books, it was Russell's writings in ethics
and politics that brought him to the attention of non-academic
audiences. His most influential books on these topics include his
Principles of Social Reconstruction (1916), On
Education (1926), Why I Am Not a Christian
(1927c), Marriage and Morals (1929), The Conquest of
Happiness (1930), The Scientific Outlook (1931),
and Power: A New Social Analysis (1938).

Since his death in 1970, Russell's reputation as a philosopher has
continued to grow. This increase in reputation has been accompanied by
a corresponding increase in scholarship. Older first-hand accounts of
Russell's life, such as Dora Russell's The Tamarisk Tree
(1975, 1981, 1985), Katharine Tait's My Father Bertrand
Russell (1975) and Clark's (1975), have been supplemented by more
recent accounts, including Caroline Moorehead's Bertrand
Russell (1992), Slater (1994) and Monk (1996, 2000).

This increase in scholarship has benefited greatly from the existence
of the
Bertrand Russell Archives
at McMaster University,
where the bulk of Russell's library and literary estate are housed,
and from the
Bertrand Russell Research Centre,
also housed at McMaster. Books such as Nicholas Griffin's
Selected Letters of Bertrand Russell (1992, 2001),
Gregory Landini's Russell's Hidden Substitutional Theory
(1998) and Bernard Linsky's The Evolution of Principia
Mathematica (2011) have all helped make public archival
material that, in the past, has been available only to
specialists. Since 1983 the
Bertrand Russell Editorial Project,
initiated by John Slater and Kenneth Blackwell, has also begun to
release authoritative, annotated editions of Russell's
Collected Papers.
When complete, this
collection will run to over 35 volumes and will bring together all of
Russell's writings, other than his correspondence and previously
published monographs.

Recent scholarship has also helped remind readers of the influence
Russell's students had on Russell's
philosophy. Ludwig Wittgenstein and
Frank Ramsey especially presented Russell with helpful criticisms of
his work and new problems to solve. Both men pushed Russell to develop
new theories in logic and epistemology. Despite the fact that
Wittgenstein was less than satisfied with Russell's comments in the
Introduction to his Tractatus Logico-Philosophicus (1921),
Michael Potter's Wittgenstein's Notes on Logic (2009) and the
introductory materials published in Russell's Theory of Knowledge:
The 1913 Manuscript (CP, Vol. 7) show the extent and
fruitfulness of the interaction between teacher and student.

Since Russell's death, debate has also taken place over the ultimate
importance of Russell's contributions, not just to philosophy, but to
other disciplines as well. Advocates of Russell's inclusion in the
canon remind readers that few have done more to advance both formal
logic and analytic philosophy. Critics of his inclusion, or at least
of his canonization, remind readers of Russell's early enthusiasm for
British imperialism (Russell 1967, 134) and of his controversial
comments about eugenics and race (Russell 1929, 259, 266). Others have
noted his apparent early antisemitism and his advocacy of a preemptive
nuclear war against the Soviet Union following World War II (Hook
1976, Stone 1981). On the issue of a preemptive war, Russell himself
later denied that he had ever advocated such a course of
action. However, after reviewing carefully the historical record,
biographer Ronald Clark comes to a different conclusion. Clark is also
unequivocal about Russell's lack of sincerity on the issue: “If
the suggestion that he deliberately tried to conceal his earlier views
is repugnant, the record does not really allow any other conclusion to
be drawn” (Clark 1975, 530). Perhaps as a result of such
observations, many readers remain undecided when attempting to
evaluate Russell's overall contribution to the intellectual life of
the twentieth century.

Monk's biography is another case in point. Monk relates Wittgenstein's
humorous suggestion that all of Russell's books should be bound in two
colours, “those dealing with mathematical logic in red –
and all students of philosophy should read them; those dealing with
ethics and politics in blue – and no one should be allowed to
read them” (Monk 2000, 278). Others, such as Peter Stone, have
argued that such caricatures are based on “a misunderstanding of
the nature of Russell as a political figure” (2003, 89) and that
“Whatever one thinks of Russell's politics, he was one of the
few public figures in the west to stand against capitalism without
succumbing to illusions about Stalinist Russia. If for no other reason
than this, Russell deserves some credit for his political
instincts” (2003, 85). (See, for example, Russell 1920 and
1922b.)

How is the ordinary reader to decide between such conflicting
evaluations? Unlike the many logical advances Russell introduced, in politics he is still usually understood to be more an advocate than a theoretician. As a result, his reputation
as a political thinker has not been as high as his reputation in logic, metaphysics and epistemology.

Even so, regardless of his many particular contributions, Russell's lasting
reputation has also benefited significantly from his constant
willingness to abandon unsupported theories and outdated beliefs. When new evidence presented itself, Russell was always among the first to take it into account:
“Against my will, in the course of my travels, the belief that
everything worth knowing was known at Cambridge gradually wore off. In
this respect,” says Russell, “my travels were very useful
to me” (1967, 133).

A short anecdote recounted in
Russell's Autobiography is also typical. As a young man, he says,
he spent part of each day for many weeks

reading Georg Cantor, and copying out the gist of him into
a notebook. At that time I falsely supposed all his arguments to be
fallacious, but I nevertheless went through them all in the minutest
detail. This stood me in good stead when later on I discovered that
all the fallacies were mine. (1967, 127)

1897, An Essay on the Foundations of Geometry,
Cambridge: At the University Press.

1900, A Critical Exposition of the Philosophy of
Leibniz, Cambridge: At the University Press.

1901, “Recent Work on the Principles of Mathematics,”
International Monthly, 4, 83–101; repr. as “Mathematics
and the Metaphysicians,” in Bertrand Russell, Mysticism and
Logic and Other Essays, New York, London: Longmans, Green & Co., 1918, 74–96; also appearing in Collected Papers, Vol. 3.

1903, The Principles of Mathematics, Cambridge: At
the University Press.

1908, “Mathematical Logic as Based on the Theory of
Types,”
American Journal of Mathematics, 30, 222–262; repr. in Bertrand
Russell, Logic and Knowledge, London: Allen
and Unwin, 1956, 59–102; also appearing in Collected Papers, Vol. 5.

1926, On Education, Especially in Early Childhood,
London: George Allen and Unwin; repr. as Education and the Good
Life, New York: Boni and Liveright, 1926; abridged as
Education of Character, New York: Philosophical Library,
1961.

Acknowledgments

Thanks are due to Kenneth Blackwell, Francisco Rodríguez-Consuegra, Fred Kroon, Jim Robinson, Russell Wahl, John Woods and several anonymous referees for their helpful comments on earlier versions of this material.